Finite Group Databasebeta

C3×#10602680 #14288609

order1920
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10602680

Splittings

HallC3×C5 ⋊ #1615
SylowC5 ⋊ C3×#1615

Subgroups

subgroupG/H
centerC22×C3#4099
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#539C2
socleC22×C3×C5#120
prime radicalC3×C5×#121C22
hypercenterC3×#539D5
hypocenterC5C3×#1615
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#539

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

201 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 14307);